Side impact protection systems that are to protect the pelvic region or the thorax region of the vehicle occupant are either integrated laterally in the backrest or in the side panel (i.e. in the vehicle door or, in the case of a two- or three-door vehicle, in the region of the rear-seat occupants in the side panel itself). The known gas bag modules are very thick when the gas bag is packed because the gas bag is folded in several directions and has a compressed pack volume. When unfolding it either emerges from the backrest and unfolds towards the front or from the side-panel covering which has a predetermined opening line. The known side gas bags for the thorax and pelvic regions have a considerable depth in the inflated state (horizontal, transverse to the direction of travel) and therefore there is a risk of, for example, sleeping occupants who have placed themselves against the side panel being injured by the deploying gas bag. Also, the covering which might tear open represents a certain potential danger because it also moves in the direction towards the occupants.